C-x C-b will open the *Buffer List* buffer. In that buffer, you can navigate with the usual keys C-p, C-n, up-arrow, down-arrow, etc.

Browsing a directory is as simple as editing a file. Just open the directory instead of the file. On my Linux machine, C-x C-f /tmp ENTER opens a directory while C-x C-f /tmp/myfile ENTER opens a file.

M-x speedbar (speedbar website) will pop up an emacs frame that lists the contents of the current directory depending on the buffer you're in. The frame is small and stays out of the way so you can always glance at it while you're editing files. It also can filter this display based on file type using the variable speedbar-supported-extension-expressions. To see all the speedbar options, type M-x customize-group RET speedbar RET.

C-x b TAB will give you an auto complete with all open buffers. Alternatively, click on the Buffers menu item if you are in a windowed version (not sure if there is a terminal equivalent of that).

EDIT: Also C-x C-f will let you open a file, and you can use TAB for autocomplete, then TAB again to view files/directories in that current directory (assuming the first tab did not autocomplete something).